Non-unitary representations of nilpotent groups, I: Cohomologies, extensions and neutral cocycles

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Kissin, Edward ; Shulman, Victor S. (2015)

Let λbe a finite-dimensional representation of a connected nilpotent group Gand Ube a unitary representation of G. We investigate the structure of the extensions of λby Uand, correspondingly, the group H1(λ, U)of 1-cohomologies. A spectral criterion of triviality of H1(λ, U)is proved and systematically used in the study of various types of decomposition of the extensions. We consider a special type of (λ, U)-cocycles – neutral cocycles, which play a crucial role in the theory of J-unitary representations of groups on Pontryagin Πk-spaces.
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